On the geometry of exceptional sets in Manin's conjecture

Manin's conjecture is a conjectural asymptotic formula for the counting function of rational points on a Fano variety, and it predicts an explicit asymptotic formula in terms of geometric invariants of the underlying variety after removing an exceptional set. In this talk I would like to discuss the geometry of this exceptional set using birational geometry, e.g., the minimal model program. This is joint work with Brian Lehmann.